Can't really see the fine details too well, but here's how I would do it. PVC Pipe for the Barrel, Insulation Foam Board for the details on it, Styrene or Sintra for the Grip and trigger assembly, if I did this I would even rig it with a spring and rig it to the trigger so the barrel could fire a tennis ball.

Keep in mind, many cons don't allow items capable of firing anything, not even a Nerf gun. Though making that thing firable would be hella fun (potato cannon fantasies ^_^).

Foam-core could be used for many of the details to save you some time on planing it to the proper thickness.

Rigging LEDs is pretty simple. The circuit is just a battery an LED and a resistor of the appropriate rating, you can find the instructions online pretty quick. I recommend a proper battery box from radio shack (or salvaged from a toy) and actually bothering to solder the contacts. Cheap soldering irons are cheap and work just fine. Read/view tutorials on how to solder, if you follow instructions it's easy. Drill a hole where you want the LEDs and secure them in place with hotglue so you can remove it if there is need for adjustment. Run the wires and hide the battery box somewhere discreet. You can either integrate a switch, or just pull out the battery when you aren't using it.

I'm probably waaaay late, but here's what I'm doing for the original Rock Cannon. I'm basing it off this tutorial: http://www.youtube.com/watch?v=lZWXU...ure=plpp_video
I'm using a cardboard tube from Home Depot as the main barrel, and then I'm actually using a Quakers oatmeal tub as the smaller tube. In the tutorial, he has a bunch of funky shapes on it, but you can just cut all those off and such.

I'm not sure about the lights, but it looks like someone else has already covered that.